The paper proposes a simple structure of high−power solid−state transformers (SSTs) able to control the energy flow in critical lines of the medium−voltage (20 kV) distribution grid. With an increasing number of renewable intermittent sources connected at the nodes of the meshed distribution grid and a reduced number of nodes connected to large power plants, the distribution grid stability is more and more difficult to achieve. Control of the energy flow in critical lines can improve the stability of the distribution grid. This control can be provided by the proposed high−power SSTs operating a 20 kV with powers over 10 MW. This function is difficult to achieve with standard SST technologies that operate at high frequencies. These devices are made with expensive magnetic materials (amorphous or nanocrystalline cores) and a limited power by SST cells. The required total power is reached by assembling many SST cells. On the other hand, existing SST designs are mainly aimed at reducing the equipment’s size and it is difficult to design small objects able to operate at high voltages. The authors propose to use cores made with grain−oriented electrical steel (GOES) thin strips assembled in wound cores. Experimental results obtained, with GOES wound cores, show that the core losses are lower for a square voltage than for a sine one. This counterintuitive result is explained with an analytical calculus of eddy currents and confirmed by a non−linear time−stepping simulation. Therefore, simple converter structures, operating with rectangular voltages and low switching losses, are the best solutions. Experimental results also show that the core losses decrease with temperature. Consequently, high−power SST cells can be made with transformers whose GOES cores are hotter than coils for reducing core losses and keeping copper losses at low levels. The paper proposes an appropriate transformer mechanical structure that avoids any contact between the hot GOES wound core and the winding, with a specific cooling system and thermal insulation of the hot GOES wound core. The proposed design makes it possible to build SST cells over 1MW and full SSTs over 10 MW at moderate costs.